1.23 Find the characteristic polynomial of a matrix

\[ \left ( {\begin {array} [c]{ccc}1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 0 \end {array}} \right ) \]

Mathematica

a = {{1,2,3},{4,5,6},{7,8,0}}; 
CharacteristicPolynomial[a,x]
 

\[ -x^3+6 x^2+72 x+27 \]

Matlab

Note: Matlab and Maple generated characteristic polynomial coefficients are negative to what Mathematica generated.

But the sign difference is not important.

clear all; 
A=[1 2 3;4 5 6;7 8 0]; 
 
p=poly(A) 
poly2str(p,'x')
 

p = 
 1.0000 -6.0000 -72.0000 -27.0000 
ans = 
 x^3 - 6 x^2 - 72 x - 27
 

Maple

restart; 
A:=Matrix([[1,2,3],[4,5,6],[7,8,0]]); 
LinearAlgebra:-CharacteristicPolynomial(A,x)
 

\[ x^{3}-6 x^{2}-72 x -27 \]